(a)[4]
Find the probability that a randomly selected female snake of this species has a length between $50\text{ cm}$ and $60\text{ cm}$.
(b)[5]
The lengths of male snakes of this species are also normally distributed. A scientist records the lengths of a random sample of $200$ male snakes of this species. He finds that $32$ have lengths less than $45\text{ cm}$ and $17$ have lengths more than $56\text{ cm}$. Find estimates for the mean and standard deviation of the lengths of male snakes of this species.